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Angular momentum of spinning bodies leads to their remarkable interactions with fields, waves, fluids, and solids. Orbiting celestial bodies, balls in sports, liquid droplets above a hot plate, nanoparticles in optical fields, and spinning quantum particles exhibit nontrivial rotational dynamics. Here, we report self-guided propulsion of magnetic fast-spinning particles on a liquid surface in the presence of a solid boundary. Above some critical spinning frequency (higher rotational Reynolds numbers), such particles generate localized 3D vortices and form composite spinner-vortex quasi-particles with nontrivial, yet robust dynamics. Such spinner-vortices are attracted and dynamically trapped near the boundaries, propagating along the wall of any shape similarly to liquid wheels. The propulsion velocity and the distance to the wall are controlled by the angular velocity of the spinner via the balance between the Magnus and wall-repulsion forces. Our results offer a new type of surface vehicles and provide a powerful tool to manipulate spinning objects in fluids.
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Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70 Hz are in qualitative agreement with the predictions of our modelling.
The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.
We analyze both theoretically and experimentally the breakup of a pendant water droplet loaded with Sodium Dodecyl Sulfate (SDS). The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the full Navier-Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses on the system dynamics for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscosity stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in that region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of the temporal evolution of the neck radius.
A charged droplet can be electrodynamically levitated in the air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square and ramp waveform at various imposed frequencies, using high-speed imaging (recorded at 100-130 thousand Frames Per Second (fps)). It is observed that the drop surface oscillates in sphere-prolate-sphere-oblate (SPSO) mode and seldom in the sphere-prolate-sphere (SPS) mode depending on the intricate interplay of various forces due to charge(q), the intensity of applied field ($Lambda$) and shift of the droplet from the geometric center of the trap ($z_{shift}$). The Fast Fourier Transformation (FFT) analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet is found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral (BI) simulations in the potential flow limit and the results are found to be in a reasonable agreement.
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.
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